For important classes of symmetrically distributed random variables X the smallest constants C[alpha] are computed on the right-hand side of Chebyshev's inequality P(X[greater-or-equal, slanted]t)[less-than-or-equals, slant]C[alpha]EX[alpha]/t[alpha]. For example if the distribution of X is a...

The asymptotic independence and exponentiality of 'pure head run' stopping times will be proved.

The power of the convexity method is demonstrated by proving Qi and Diaz-Metcalf type inequalities.

In a string of n independent coin tosses we consider the difference between the lengths of the longest blocks of consecutive heads resp. tails. We prove that this quantity has an a.s. logarithmic limit distribution as n -- [infinity], though it does not converge in distribution in the ordinary...

Web sites invest significant resources in trying to influence their visibility in online search results. We study the economic incentives of Web sites to invest in this process known as search engine optimization. We focus on methods that improve sites' ranking among the search results without...

The Internet has increased the flexibility of retailers, allowing them to operate an online arm in addition to their physical stores. The online channel offers potential benefits in selling to customer segments that value the convenience of online shopping, but it also raises new challenges....

A key property of the World Wide Web is the possibility for firms to place virtually costless links to third-party content as a substitute or complement to their own content. This ability to hyperlink has enabled new types of players, such as search engines and content aggregators, to...

Paid placements on search engines reached sales of nearly $11 billion in the United States last year and represent the most rapidly growing form of online advertising today. In its classic form, a search engine sets up an auction for each search word in which competing websites bid for their...

We model the commercial World Wide Web as a directed graph that emerges as the equilibrium of a game in which utility maximizing websites purchase (advertising) in-links from each other while also setting the price of these links. In equilibrium, higher content sites tend to purchase more...